A geometric method for isomorphically transforming the shape of biological structures expressed as two dimensional projections is being applied to tracings of cephalograms to determine constraints underlying growth and development. The rationale underlying this effort is based on the assumption that the relatively small amount of systematic progress in quantitative morphology may be attributed to a lac of coordinate independent bases for mathematical description. Symmetric-axis geometry provides a promising alternative to conventional cephalometric descriptions which has lead to the discovery of fixed angular relationships in lateral projections of the human mandible. The associated angles appear to be independent of age within and between individuals. Preliminary findings applied to the mandibular shape of other species suggest that homologous angles may be invariant likewise.